In mathematics, a pointed set is a set with a distinguished element, which is called the basepoint. Maps of pointed sets (based maps) are those functions that map one basepoint to another, i.e. a map such that . This is usually denoted
- .
Pointed sets may be regarded as a rather simple algebraic structure. In the sense of universal algebra, they are structures with a single nullary operation which picks out the basepoint.
The class of all pointed sets together with the class of all based maps form a category.
A pointed set may be seen as a pointed space under the discrete topology or as a vector space over the field with one element.
Famous quotes containing the words pointed and/or set:
““Courage!” he said, and pointed toward the land,
“This mounting wave will roll us shoreward soon.”
In the afternoon they came unto a land
In which it seemed always afternoon.”
—Alfred Tennyson (1809–1892)
“It may be that the most interesting American struggle is the struggle to set oneself free from the limits one is born to, and then to learn something of the value of those limits.”
—Greil Marcus (b. 1945)